Cohen, Friedland, Kato, and Kelly conjectured that F(t)≡log r(eAteBt) is convex for real t when A is nonnegative and B is diagonal; here r is the spectral radius. While the conjecture is correct for dimension n=1 or 2, it is shown here to be false for n≥3. Similarly t → logTrace(eAteBt)k need not be convex when n≥3.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics